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Prediction of pKas of Titratable Residues in Proteins Using a Poisson-Boltzmann Model of the Solute-Solvent System
J. Antosiewicz, E. Błachut-Okrasińska, T. Grycuk, J.M. Briggs, S.T. Wlodek, B. Lesyng and J.A. McCammon
This article provides an overview of an algorithm used for the prediction of ionization constants of titratable residues in proteins. The algorithm is based on an assumption that the difference in protonation behavior of a given group in an isolated state in solution, for which the ionization constant is assumed to be known, and the protonation behavior in the protein environment is purely electrostatic in origin. Calculations of the relevant electrostatic free energies are based on the Poisson-Boltzmann (PB) model of the protein-solvent system and the finite-difference solution to the corresponding PB equation. The resultant multiple site titration problem is treated by one of two methods. The first is a Hybrid approach, based on collecting ionizable groups into clusters. The second method is a Monte Carlo approach based on the Metropolis algorithm for extracting a sufficient number of low-energy ionization states out of all possible states, to obtain a correct estimation of thermodynamic properties of the system. As examples of applications, we present the overall accuracy of predicted ionization constants for about 50 groups in 4 proteins, changes in the average charge of bovine pancreatic trypsin inhibitor at pH 7 along a molecular dynamics trajectory, and finally, we discuss some preliminary results obtained for protein kinases and protein phosphatases.
Are Molecular Motions Important for Function?
J. Andrew McCammon
Many of the functions of biopolymers are governed by the time dependence of their internal motions. Several examples are described. It is concluded that evolution has selected biological molecules for dynamical as well as structural properties.
What Do We Need to Know about Proteins and Nucleic Acids?
K.A. Dill, J. Deisenhofer, G.R. Fleming, H. Frauenfelder, K. Gerwert, J.A. McCammon and H. Michel
What do we need to know about the structures of proteins and nucleic acids? What do we need to know about their mechanisms of action? What methodological advances in theory/simulation/experiment will lead to progress in our understanding of structure, dynamics, and function? We explore these issues here.
Conformational Transitions of Proteins from Atomistic Simulations
V. Helms and J.A. McCammon
The function of many important proteins comes from their dynamic properties, and their ability to undergo conformational transitions. These may be small loop movements that allow access to the protein's active site, or large movements such as those of motor proteins that are implicated with muscular extension. Yet, in spite of the increasing number of three-dimensional crystal structures of proteins in different conformations, not much is known about the driving forces of these transitions. As an initial step towards exploring the conformational and energetic landscape of protein kinases by computational methods, intramolecular energies and hydration free energies were calculated for different conformations of the catalytic domain of cAMP-dependent protein kinase (cAPK) with a continuum (Poisson) model for the electrostatics. In this paper, we will put the previous results into context and discuss possible extensions into the dynamic regime.
Ewald Artifacts in Computer Simulations of Ionic Solvation and Ion-Ion Interaction: A Continuum Electrostatics Study
Philippe H. Hünenberger and J. Andrew McCammon
The use of Ewald and related methods to handle electrostatic interactions in explicit solvent simulations of solutions imposes an artificial periodicity on systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of those computer simulations. In the present study, we propose a general method based on continuum electrostatics to investigate the nature and magnitude of periodicity-induced artifacts. As a first example, this scheme is applied to the solvation free energy of a spherical ion. It is found that artificial periodicity reduces the magnitude of the ionic solvation free energy, because the solvent in the periodic copies of the central unit cell is perturbed by the periodic copies of the ion, thus less available to solvate the central ion. In the limit of zero ionic radius and infinite solvent permittivity, this undersolvation can be corrected by adding the Wigner self-energy term to the solvation free energy. For ions of a finite size or a solvent of finite permittivity, a further correction is needed. An analytical expression for this correction is derived using continuum electrostatics. As a second example, the effect of artificial periodicity on the potential of mean force for the interaction between two spherical ions is investigated. It is found that artificial periodicity results in an attractive force between ions of like charges, and a repulsive force between ions of opposite charges. The analysis of these two simple test cases reveals that two individually large terms, the periodicity-induced perturbations of the Coulomb and solvation contributions, often cancel each other significantly, resulting in an overall small perturbation. Three factors may prevent this cancellation to occur and enhance the magnitude of periodicity-induced artifacts: (i) a solvent of low dielectric permittivity, (ii) a solute cavity of non-negligible size compared to the unit cell size, and (iii) a solute bearing a large overall charge.
Calculation of the pKa Values for the Ligands and Side Chains of Escherichia coli D-Alanine:D-Alanine Ligase
Heather A. Carlson, James M. Briggs and J. Andrew McCammon
Poisson-Boltzmann electrostatics methods have been used to calculate the pKa shifts for the ligands and titratable side chains of D-alanine:D-alanine ligase of the ddlb gene of E. coli (DdlB). The focus of this study is to determine the ionization state of the second D-alanine (D-ala2) in the active site of DdlB. The pKa of the amine is shifted over five pKa units more alkaline in the protein, clearly implying that D-ala2 is bound to DdlB in its zwitterionic state and not in the free-base form as had been previously suggested. Comparisons are made to the depsipeptide ligase from the vancomycin-resistance cascade, VanA. It is suggested that VanA has different enzymatic properties due to a change in binding specificity rather than altered catalytic behavior and that the specificity of binding D-lactate over D-ala2 may arise from the difference in ionization characteristics of the ligands.
Phosphorylation Stabilizes the N-Termini of α-Helices
Jason L. Smart and J. Andrew McCammon
The role of phosphorylation in stabilizing the N-termini of α-helices is examined using computer simulations of model peptides. The models comprise either a phosphorylated or unphosphorylated serine at the helix N-terminus, followed by nine alanines. Monte Carlo/Stochastic Dynamics simulations were performed on the model helices. The simulations revealed a distinct stabilization of the helical conformation at the N-terminus after phosphorylation. The stabilization was attributable to favorable electrostatic interactions between the phosphate and the helix backbone. However, direct helix capping by the phosphorylated sidechain was not observed. The results of the calculations are consistent with experimental evidence on the stabilization of helices by phosphates and other anions.
Determinants of Ligand Binding to cAMP-Dependent Protein Kinase
Philippe H. Hünenberger, Volkhard Helms, Narendra Narayana, Susan S. Taylor and J. Andrew McCammon
Protein kinases are essential for the regulation of cellular growth and metabolism. Since their dysfunction leads to debilitating diseases, they represent key targets for pharmaceutical research. The rational design of kinase inhibitors requires an understanding of the determinants of ligand binding to these proteins. In the present study, a theoretical model based on continuum electrostatics and a surface-area dependent non-polar term is used to calculate binding affinities of balanol derivatives, H-series inhibitors and ATP analogs towards the catalytic subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The calculations reproduce most of the experimental trends, and provide insight into the driving forces responsible for binding. Non-polar interactions are found to govern protein-ligand affinity. Hydrogen bonds represent a negligible contribution, because hydrogen bond formation in the complex requires the desolvation of the interacting partners. However, the binding affinity is decreased if hydrogen-bonding groups of the ligand remain unsatisfied in the complex. The disposition of hydrogen-bonding groups in the ligand is therefore crucial for binding specificity. These observations should be valuable guides in the design of potent and specific kinase inhibitors.
Molecular Dynamics Simulations of the Hyperthermophilic Protein Sac7d from Sulfolobus acidocaldarius: Contribution of Salt Bridges to Thermostability
Paul I.W. de Bakker, Philippe H. Hünenberger and J. Andrew McCammon
Hyperthermophilic proteins often possess an increased number of surface salt bridges compared to their mesophilic homologues. Yet, salt bridges are generally thought to be of minor importance in protein stability at room temperature. In an effort to understand why this may no longer be true at elevated temperatures, we performed molecular dynamics simulations of the hyperthermophilic protein Sac7d at 300 K, 360 K, and 550 K. The three trajectories are stable on the nanosecond timescale, as evidenced by the analysis of several time-resolved properties. The simulations at 300 K and (to a lesser extent) 360 K are also compatible with NOE-derived distances. Raising the temperature from 300 K to 360 K results in a less favorable protein-solvent interaction energy, and a more favorable intraprotein interaction energy. Both effects are almost exclusively electrostatic in nature and dominated by contributions due to charged side chains. The reduced solvation is due to a loss of spatial and orientational structure of water around charged side chains, which is a consequence of the increased thermal motion in the solvent. The favorable change in the intraprotein Coulombic interaction energy is essentially due to the tightening of salt bridges. Assuming that charged side chains are on average more distant from one another in the unfolded state than in the folded state, it follows that salt bridges may contribute to protein stability at elevated temperatures because (i) the solvation free energy of charged side chains is more adversely affected in the unfolded state than in the folded state by an increase in temperature, and (ii) due to the tightening of salt bridges, unfolding implies a larger unfavorable increase in the intraprotein Coulombic energy at higher temperature. Possible causes for the unexpected stability of the protein at 550 K are also discussed.
Dynamic and Rotational Analysis of Cryptophane Host-Guest Systems: Challenges of Describing Molecular Recognition
Paul D. Kirchhoff, Jean-Pierre Dutasta, André Collet and J. Andrew McCammon
Cryptophanes are aromatic hosts which bind a variety of guests. Here, we describe three 25 ns molecular dynamics simulations of a particular cryptophane in water. Simulations have been conducted on the uncomplexed cryptophane, the cryptophane-tetramethylammonium ion (TMA+) complex, and the cryptophane-neopentane (NEO) complex. TMA+ and NEO are both tetrahedral molecules and are nearly isomorphic. In the current study, we examine how the presence of these guests influences motions of the host. Also examined are the preferred orientations and the motions of the guests relative to the cryptophane. This study demonstrates some of the many challenges of describing molecular recognition.
Mouse Acetylcholinesterase Unliganded and in Complex with Huperzine A: A Comparison of Molecular Dynamics Simulations
Sylvia Tara, T.P. Straatsma and J. Andrew McCammon
A 1 ns molecular dynamics simulation of unliganded mouse acetylcholinesterase (AChE) is compared to a previous simulation of mouse AChE complexed with Huperzine A (HupA). Several common features are observed. In both simulations, the active site gorge fluctuates in size during the 1 ns trajectory, and is completely pinched off several times. Many of the residues in the gorge that formed hydrogen bonds with HupA in the simulation of the complex, now form hydrogen bonds with other protein residues and water molecules in the gorge. The opening of a "backdoor" entrance to the active site that was found in the simulation of the complex is also observed in the unliganded simulation. Differences between the two simulations include overall lower structural RMS deviations for residues in the gorge in the unliganded simulation, a smaller diameter of the gorge in the absence of HupA, and the disappearance of a side channel that was frequently present in the liganded simulation. The differences between the two simulations can be attributed, in part, to the interaction of AChE with HupA.
OOMPAA - Object-Oriented Model for Probing Assemblages of Atoms
Gary A. Huber and J. Andrew McCammon
OOMPAA is a library of C++ classes that can be used to generate molecular simulation software. The core of OOMPAA includes scripts for generating user-defined atom classes, as well as classes that represent groups of atoms, like bonds, aromatic rings, lists of atoms, etc. It has easy and efficient parameter lists and facilities for allowing one to treat attributes of lists of atoms (like positions) as large vectors. OOMPAA is designed to grow; additions include energy minimizers, integrators, facilities for dealing with protein molecules, and interfaces to established electrostatic equation solvers. It is designed with efficiency in mind; with a good optimizing C++ compiler, simulation speed can approach that of Fortran, while retaining the elegance of expression afforded by object-oriented programming.
Association and Dissociation Kinetics of Bobwhite Quail Lysozyme with Monoclonal Antibody HyHEL-5
K. Asish Xavier, Shawn M. McDonald, J. Andrew McCammon and Richard C. Willson
The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and its complexes with various species-variant and mutant lysozymes have been the subject of considerable experimental and theoretical investigation. The affinity of HyHEL-5 for bobwhite quail lysozyme (BWQL) is over 1000-fold lower than its affinity for the original antigen, hen egg lysozyme (HEL). This difference is believed to arise almost entirely from the replacement in BWQL of the structural and energetic epitope residue Arg68 by lysine. In this study, the association and dissociation kinetics of BWQL with HyHEL-5 were investigated under a variety of conditions and compared with previous results for HEL. HyHEL-5-BWQL association follows a bimolecular mechanism and the dissociation of the antibody-antigen complex is a first-order process. Changes in ionic strength (from 27 to 500 mM) and pH (from 6.0 to 10.0) produced about a 2-fold change in the association and dissociation rates. The effect of viscosity modifiers on the association reaction was also studied. The large difference in the HEL and BWQL affinities for HyHEL-5 is essentially due to differences in the dissociation rate constant.
Situs: A Package for Docking Crystal Structures into Low-Resolution Maps from Electron Microscopy
Willy Wriggers, Ronald A. Milligan and J. Andrew McCammon
Three-dimensional image reconstructions of large-scale protein aggregates are routinely determined by electron microscopy (EM). We combine low-resolution EM data with high-resolution structures of proteins determined by X-ray crystallography. A set of visualization and analysis procedures, termed the Situs package, has been developed to provide an efficient and robust method for the localization of protein subunits in low-resolution data. Topology-representing neural networks are employed to vector-quantize and to correlate features within the structural data sets. Microtubules decorated with kinesin-related ncd motors are used as model aggregates to demonstrate the utility of this package of routines. The precision of the docking has allowed for the extraction of unique conformations of the macromolecules and is limited only by the reliability of the underlying structural data.
Non-Boltzmann Rate Distributions in Stochastically Gated Reactions
Nathan A. Baker and J. Andrew McCammon
Recently, a new mechanism for reaction selectivity, arising from conformational gating of the reactions, has been reported in the acetylcholinesterase system. Fluctuations in the enzyme are thought to greatly slow the access of molecules larger than the normal substrate to the active site region. By assuming the gate fluctuations occur as a Brownian process in a harmonic well, it is possible to approximate the reaction rates for various limiting cases of substrate size. However, it is not possible to simplify the rates into a ratio which is equivalent to the Boltzmann distribution of states for the gate fluctuations.
Internal Dynamics of Green Fluorescent Protein
Volkhard Helms, T.P. Straatsma and J. Andrew McCammon
A 1 ns molecular dynamics simulation was performed to study the dynamic behavior of wild type green fluorescent protein from Aequorea victoria. We find the protein to be remarkably rigid, both overall, because the cylindrical beta-barrel provides a stable framework, but also on an atomic level in the immediate surrounding of the chromophore. Here, a tight H-bond network is formed mainly involving six internal water molecules. The perfect barrel is interrupted only between beta-strands 7 and 8 where contact is made via side chain interactions, and we investigated the dynamic behavior of this region in detail. After ca. 320 ps of simulation, an Arginine residue, initially sticking out into solution, folded over the cleft to form a H-bond with a backbone oxygen atom on the opposite strand. This contact appears important for stabilization of the overall protein architecture.
Effect of Artificial Periodicity in Simulations of Biomolecules under Ewald Boundary Conditions: A Continuum Electrostatics Study
P.H. Hünenberger and J.A. McCammon
Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since it may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity, (ii) a solute size which is non-negligible compared to the size of the unit cell, and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.
Molecular Dynamics Studies on the HIV-1 Integrase Catalytic Domain
Roberto D. Lins, James M. Briggs, T.P. Straatsma, Heather A. Carlson, Jason Greenwald, Senyon Choe and J. Andrew McCammon
The HIV-1 integrase, which is essential for viral replication, catalyzes the insertion of viral DNA into the host chromosome thereby recruiting host cell machinery into making viral proteins. It represents the third main HIV enzyme target for inhibitor design, the first two being the reverse transcriptase and the protease. Two 1 ns molecular dynamics simulations have been carried out on completely hydrated models of the HIV-1 integrase catalytic domain, one with no metal ions and another with one magnesium ion in the catalytic site. The simulations predict that the region of the active site that is missing in the published crystal structures has more secondary structure than previously thought. The flexibility of this region has been discussed with respect to the mechanistic function of the enzyme. The results of these simulations will be used as part of inhibitor design projects directed against the catalytic domain of the enzyme.
Polarization Around an Ion in a Dielectric Continuum with Truncated Electrostatic Interactions
Nathan A. Baker, Philippe H. Hünenberger and J. Andrew McCammon
In order to reduce the computational effort and to allow for the use of periodic boundary conditions, electrostatic interactions in explicit solvent simulations of molecular systems do not obey Coulomb's law. Instead, a number of "effective potentials" have been proposed, including truncated Coulomb, shifted, switched, reaction-field corrected, or Ewald potentials. The present study compares the performance of these schemes in the context of ionic solvation. To this purpose, a generalized form of the Born continuum model for ion solvation is developed, where ion-solvent and solvent-solvent interactions are determined by these effective potentials instead of Coulomb's law. An integral equation is formulated for calculating the polarization around a spherical ion from which the solvation free energy can be extracted. Comparison of the polarizations and free energies calculated for specific effective potentials and the exact Born result permits an assessment of the accuracy of these different schemes. Additionally, the present formalism can be used to develop corrections to the ionic solvation free energies calculated by molecular simulations implementing such effective potentials. Finally, an arbitrary effective potential is optimized to reproduce the Born polarization.
Shedding Light on the Dark and Weakly Fluorescent States of Green Fluorescent Proteins
Wolfgang Weber, Volkhard Helms, J. Andrew McCammon and Peter W. Langhoff
Recent experiments on various similar green fluorescent protein (GFP) mutants at the single-molecule level and in solution provide evidence of previously unknown short- and long-lived "dark" states and of related excited-state decay channels. Here, we present quantum chemical calculations on cis-trans photoisomerization paths of neutral, anionic, and zwitterionic GFP chromophores in their ground and first single excited states which explain the observed behaviors from a common perspective. The results suggest that favorable radiationless decay channels can exist for the different protonation states along these isomerizations, which apparently proceed via conical intersections. These channels are suggested to rationalize the observed dramatic reduction of fluorescence in solution. The observed single-molecule fast blinking is attributed to conversions between the fluorescent anionic and the dark zwitterionic forms while slow switching is attributed to conversions between the anionic and the neutral forms. The predicted nonadiabatic crossings are seen to rationalize the origins of a variety of experimental observations on a common basis, and may have broad implications for photobiophysical mechanisms in GFP.
Molecular Dynamics of Mouse Acetylcholinesterase Complexed with Huperzine A
Sylvia Tara, Volkhard Helms, T.P. Straatsma and J. Andrew McCammon
Two molecular dynamics simulations were performed for a modeled complex of mouse acetylcholinesterase (AChE) liganded with Huperzine A (HupA). Analysis of these simulations shows that HupA shifts in the active site towards Tyr 337 and Phe 338 and that several residues in the active site area reach out to make hydrogen bonds with the inhibitor. Rapid fluctuations of the gorge width are observed, ranging from widths that allow substrate access to the active site, to pinched structures that do not allow access of molecules as small as water. Additional openings or channels to the active site are found. One opening is formed in the side wall of the active site gorge by residues Val 73, Asp 74, Thr 83, Glu 84, and Asn 87. Another opening is formed at the base of the gorge by residues Trp 86, Val 132, Glu 202, Gly 448, and Ile 451. Both of these openings have been observed separately in the T. californica form of the enzyme. These channels could allow transport of waters and ions to and from the bulk solution.
Dynamical Properties of Fasciculin-2
Nathan A. Baker, Volkhard Helms and J. Andrew McCammon
Fasciculin-2 (FAS2) is a potent protein inhibitor of the hydrolytic enzyme acetylcholinesterase. A 2 ns isobaric-isothermal ensemble molecular dynamics simulation of this toxin was performed to examine the dynamic structural properties which may play a role in this inhibition. Conformational fluctuations of the FAS2 protein were examined by a variety of techniques to identify flexible residues and determine their characteristic motion. The tips of the toxin "finger" loops and the turn connecting loops I and II were found to fluctuate, while the rest of the protein remained fairly rigid throughout the simulation. Finally, the structural fluctuations were compared to NMR data of fluctuations on a similar timescale in a related three-finger toxin. The molecular dynamics results were in good qualitative agreement with the experimental measurements.
Molecular Dynamics of Cryptophane and its Complexes with Tetramethylammonium and Neopentane Using a Continuum Solvent Model
Michael J. Potter, Paul D. Kirchhoff, Heather A. Carlson and J. Andrew McCammon
Time-scales currently obtainable in explicit-solvent molecular dynamics simulations are inadequate for the study of many biologically important processes. This has led to increased interest in the use of continuum solvent models. In order for such models to be used effectively, it is important that their behavior relative to explicit simulation be clearly understood. Accordingly, 5 ns stochastic dynamics simulations of a derivative of cryptophane-E alone, and complexed with tetramethylammonium and neopentane were carried out. Solvation electrostatics were accounted for via solutions to the Poisson equation. Non-electrostatic aspects of solvation were incorporated using a surface-area-dependent energy term. Comparison of the trajectories to those from previously reported 25 ns explicit-solvent simulations shows that use of a continuum solvent model results in enhanced sampling. Use of the continuum solvent model also results in a considerable increase in computational efficiency. The continuum solvent model is found to predict qualitative structural characteristics which are similar to those observed in explicit solvent. However, some differences are significant, and optimization of the continuum parameterization will be required for this method to become an efficient alternative to explicit-solvent simulation.
Poisson-Boltzmann Model Studies of Molecular Electrostatic Properties of the cAMP-Dependent Protein Kinase
Elżbieta Błachut-Okrasińska, Bogdan Lesyng, James M. Briggs, J. Andrew McCammon and Jan M. Antosiewicz
Protonation equilibria of residues important in the catalytic mechanism of a protein kinase were analyzed on the basis of the Poisson-Boltzmann electrostatic model along with a cluster-based treatment of the multiple titration state problem. Calculations were based upon crystallographic structures of the mammalian cAMP dependent protein kinase (PKA), one representing the so called closed form of the enzyme and the other representing an open conformation.
It was predicted that at pH 7 the preferred form of the phosphate group at the catalytically essential threonine 197 (P-Thr197) in the closed form is dianionic, whereas in the open form a monoanionic ionization state is preferred. This dianionic state of P-Thr197, in the closed form, is stabilized by interactions with ionizable residues His87, Arg165 and Lys189.
Our calculations predict that the hydroxyl of the Ser residue in the peptide substrate is very difficult to ionize, both in the closed and open structures of the complex. Also, the supposed catalytic base, Asp166, does not seem to have a pKa appropriate to remove the hydroxyl group proton of the peptide substrate. However, when Ser of the peptide substrate is forced to remain ionized, the predicted pKa of Asp166 increases strongly which suggests that the Asp residue is a likely candidate to attract the proton if the Ser residue becomes deprotonated, possibly during some structural change preceding formation of the transition state.
Finally, in accord with suggestions made on the basis of the pH-dependence of kinase kinetics, our calculations predict that Glu230 ahnd His87 are the residues responsible for the molecular pKas of 6.2 and 8.5, observed in the experiment.
Computer Simulation of Protein-Protein Association Kinetics: Acetylcholinesterase-Fasciculin
Adrian H. Elcock, Razif R. Gabdoulline, Rebecca C. Wade and J. Andrew McCammon
Computer simulations were performed to investigate the role of electrostatic interactions in promoting fast association of acetylcholinesterase with its peptidic inhibitor, the neurotoxin fasciculin. The encounter of the two macromolecules was simulated with the technique of Brownian dynamics (BD), using atomically detailed structures, and association rate constants were calculated for the wild type and a number of mutant proteins. In a first set of simulations, the ordering of the experimental rate constants for the mutant proteins was correctly reproduced, although the absolute values of the rate constants were overestimated by a factor of around 30. Rigorous calculations of the full electrostatic interaction energy between the two proteins indicate that this overestimation of association rates results at least in part from approximations made in the description of interaction energetics in the BD simulations. In particular, the initial BD simulations neglect the unfavourable electrostatic desolvation effects resulting from the exclusion of high dielectric solvent that accompanies the approach of two low dielectric proteins. This electrostatic desolvation component is so large that the overall contribution of electrostatics to the binding energy of the complex is unlikely to be strongly favourable. Nevertheless, electrostatic interactions are still responsible for increased association rates because even if they are unfavourable in the fully-formed complex, they are still favourable at intermediate protein-protein separation distances. It therefore appears possible for electrostatic interactions to promote the kinetics of binding even if they do not make a strongly favourable contribution to the thermodynamics of binding. When an approximate description fo these electrostatic desolvation effects is included in a second set of BD simulations, the relative ordering of the mutant proteins is again correctly reproduced, but now association rate constants that are much closer in magnitude to the experimental values are obtained. Inclusion of electrostatic desolvation effects also improves reproduction of the experimental ionic strength dependence of the wild type associate rate.
Method for Including the Dynamic Fluctuations of a Protein in Computer-Aided Drug Design
Heather A. Carlson, Kevin M. Masukawa and J. Andrew McCammon
We have recently presented a new pharmacophore design method that allows for the incorporation of the inherent flexibility of a target active site. The flexibility of the enzymatic system is described by collecting many conformations of the uncomplexed protein; this ensemble of conformational states can come from a molecular dynamics (MD) simulation, multiple crystal structures, or many NMR structures. Binding sites that complement the active site are determined through multiple-copy calculations. These calculations are conducted for each protein conformation, providing a large collection of potential binding sites. The Cartesian coordinates from each protein conformation are overlaid through RMS fitting of essential catalytic residues, and the pharmacophore model is described by binding regions that are conserved over many protein conformations. Previously, we developed a "dynamic" pharmacophore model for HIV-1 integrase using 11 conformations of the protein from an MD simulation; the MUSIC procedure was used to calculate binding positions for methanol molecules in each configuration of the active site. Here we present "static" pharmacophore models developed with a single conformation of the protein from two new crystal structures (standard protocol for multiple-copy methods). The static models do not perform as well as the previous dynamic model in fitting known inhibitors of HIV-1 integrase. To test the applicability of the dynamic pharmacophore method and the assumption that any reliable source of protein conformations is applicable, we have now developed a second dynamic pharmacophore model based on the two crystal structures also used for the development of the static models. Though the dynamic model based on the two crystal structures does not fit as many known inhibitors as the previous dynamic model, it is a significant improvement over the static models. Even better performance is expected with the addition of more crystal structures if they become available. However, it is notable that using only two structures leads to great improvement in the models.
Annealing Accounts for the Length of Actin Filaments Formed by Spontaneous Polymerization
David Sept, Jingyuan Xu, Thomas D. Pollard and J. Andrew McCammon
We measured the lengths of actin filaments formed by spontaneous polymerization of highly purified actin monomers by fluorescence microscopy after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 um (2600 subunits), independent of the initial concentration of actin monomer. The polymerizaiton of actin is modeled using a nucleation-elongation reaction scheme. With the addition of filament annealing and fragmenting we can reproduce the observed average length over a wide range of actin concentrations. The effect of capping protein, CapZ, on the mean length is also modeled.
Technique for Developing a Pharmacophore Model that Accommodates Inherent Protein Flexibility: An Application to HIV-1 Integrase
Kevin M. Masukawa, Heather A. Carlson and J. Andrew McCammon
We present a new method for the development of pharmacophore models that account for the inherent flexibility of a target active site. The flexibility of the enzymatic system is described by collecting many conformations of the uncomplexed protein from a molecular dynamics (MD) simulation. The binding sites for functional groups that complement the active site are determined through a series of multi-unit search for interacting conformers (MUSIC) simulations. MUSIC simulations are conducted for each saved conformation of the protein, providing a large ocllection of potential binding sites. The binding sites from each protein conformation are overlaid, and the pharmacophore model is described by the conserved binding regions for the probe molecules. The "dynamic" pharmacophore model presented in this study is the first reported receptor-based pharmacophore model for HIV-1 integrase. Using standard protocol for multiple-copy simulations, "static" pharmacophore models were developed with the crystal structure that was used to initialize the MD studies and two additional crystal structures that became available after the completion of the MD study. The pharmacophore models were compared to known inhibitors of the integrase. The dynamic model compares much more favorably with the set of known inhibitors than do the static models, implying that new compounds determined with the dynamic model have a greater potential for inhibition than those identified with the static models.
Computer Simulations of Actin Polymerization Can Explain the Barbed-Pointed End Asymmetry
David Sept, Adrian H. Elcock and J. Andrew McCammon
Computer simulations of actin polymerization were performed to investigate the role of electrostatic interactions in determining polymerization rates. Atomically-detailed models of actin monomers and filaments were used in conjunction with a Brownian dynamics method. The simulations were able to reproduce the measured barbed end association rates over a range of ionic strengths and predicted a slower growing pointed end, in agreement with experiment. Similar simulations neglecting electrostatic interactions indicate that configurational and entropic factors may actually favor polymerization at the pointed end, but electrostatics interactions remove this trend. This result would indicate that polymerization at the pointed end is not only limited by diffusion, but faces electrostatic forces that oppose binding. The binding of the Actin Depolymerizing Factor (ADF) and G-actin complex to the end of a filament was also simulated. In this case, electrostatic steering effects lead to an increase in the simulated association rate. Together, the results indicate that simulations provide a realistic description of both polymerization and the binding of more complex structures to actin filaments.